DYNAMICAL PROPERTIES OF HIGH TEMPERATURE SUPERCONDUCTORS

Abstract

The well-known strange behavior of superconductivity (SC) discovered by H K Onnes evoked great curiosity and initiated a new chapter in the history of physics. The theorists and experimentalists throughout the globe have been endeavoring to understand this extraordinary phenomenon for many years. A phenomenological theory, named as Ginzburg-Landau (GL) theory successfully explained most of the aspects of superconductors in the vicinity of the transition temperature Tc. The crucial insight of GL theory is the introduction of the complex order parameter in the free energy expansion to describe the superconducting state. In this connection, Bardeen-Cooper-Schrie er (BCS) theory has found one of the most successful theory among the other theories in the conventional era, and this microscopic theory explained several characteristics of di erent superconducting materials. However, the major goal of the superconducting materials is to achieve the phenomenon of SC at room temperature. The discovery of such high temperature superconductors (HTS) is the prime requirement for today and future technology. This succeeded into massive theoretical and experimental e orts to discover new HTS. In 1986, the advent of high temperature superconductivity (HTSC) was heralded as a breakthrough discovery with the development of cuprates like La2􀀀xSrxCuO4 (Tc = 37:5 K) and YBa2Cu3O7􀀀 (Tc = 92 K). These discovered superconductors initiated a pursuit to discover HTS with a higher critical temperature. Various models have been proposed to understand the mechanism of HTS. The evolution of the theory i ii of HTSC of these superconductors and understanding of their dynamical behavior became one of the foremost leading challenges, and the quest is still on. The unit cell of HTS incorporates a large number of atoms or ions increasing the possibility of many-body interactions. The dimensionality plays a signi cant role in the mechanism of HTSC which drew the attention of many experimentalists as well as of theorists to study the mechanism of HTS. The high-temperature cuprate superconductor has a layered crystal structure which consists of conduction layers as well as charge reservoir layers. Each copper atom in the conducting planes has apical oxygen atoms which display the ample in uence of anharmonicities as well as the e ect of defects. The study of phonons exhibits a central role in characterizing the many dynamical properties of HTS which need to be studied to a satisfactory extent. The careful investigation of anharmonicity is complicated from a theoretical point of view because of an anharmonic disturbance is considerably signi cant at very low temperature. The role of doping (impurity) in HTS play a crucial part to control the superconducting properties of copper oxide crystals. Moreover, the in uences of disorders and defects can be thoroughly understood which extremely modify the frequency (energy) spectrum and dynamical characteristics of crystals. The appearance of defects and anharmonicities leads to signi cant modi cations to the density of states in a crystal. Electron-phonon (ep) coupling is also a remarkable e ect for describing the features of HTS. Several mechanisms to understand the strange phenomenon of HTSC have been proposed that includes the formation of pairs known as Cooper pairs or pairons (e-pairons and h-pairons) which is a consequence of electron or hole pairing via weak to strong coupling phenomena also mediated by phonons. The role of electrons and phonons appear to be relevant during the formation of pairons (or Cooper pair) in the transition region, instead of heat transport. The ep-interactions in HTS display phononic as well as electronic characteristics via the density of states. iii The density of states plays a pivotal role in the study of a large number of dynamical properties; especially, the electronic and phononic heat capacities, thermal transport, etc. of HTS. Remarkably, the evaluation of heat capacity provides a measure of the strength of ep-coupling which may lead to prompt to understand the pairon mechanism with profound insight in HTS. In this dissertation, we have investigated renormalized phonon frequency spectrum, the density of states of phonons and electrons, and the heat capacity of phonons and electrons for La2􀀀xSrxCuO4 and YBa2Cu3O7􀀀 superconductor considering e ects of anharmonicities, defects, ep-interactions in HTS in a new framework based on the many-body quantum dynamics of electrons and phonons. This investigation manifests a detailed theoretical approach to understand the underlying physics of the phenomenon of HTSC. This investigation reports that these e ects are essential and suitable for the estimations of the dynamical properties of HTS. The organization of this thesis work is as follows: Chapter 1 describes a brief overview of the historical advancements of SC and a precise outline of recent developments in the area of SC. The motivation for present research work with the state of art of the problem and the aspects of the theory has presented brie y to understand the outlay of this thesis. Chapter 2 is devoted to the detailed description of the methodology. The new impurity induced anharmonic electron-phonon problem has been theoretically dealt using the many-body theory of Green's functions (GF). A model Hamiltonian (without considering BCS Hamiltonian) consists of multi-phonon interactions viz. electrons, phonons, electron-phonon, anharmonicities and defects to develop the double-time thermodynamic GF theory of phonons and electrons. Born-Mayer-Huggins (BMH) potential appears most suitable potential to study the dynamical properties of such HTS and shows its signi cance in establishing the importance of anharmonicities as iv well as defects. The renormalized phonon frequency spectrum of La2􀀀xSrxCuO4 and YBa2Cu3O7􀀀 HTS have been investigated in the new framework. Chapter 3 deals with the evaluation of renormalized and generalized density of states of phonons and electrons (RPDOS, REDOS, GPDOS, and GEDOS) have been developed using Lehmann's representation. This theoretical approach extraordinarily divides the RPDOS and GPDOS into diagonal and non-diagonal components which chie y depends on mass change parameter. The obtained results have been utilized to investigate the renormalized and generalized DOS of phonons and electrons for La2􀀀xSrxCuO4 and YBa2Cu3O7􀀀 . The theoretical investigations of GPDOS and GEDOS with the variation of doping and temperature for both cuprate superconductor has been reported. Chapter 4 aims to investigate the anomalous behavior of the electronic heat capacity (EHC) with the help of the RPDOS through the average electron energy of the system. The present theory of EHC reports that it shows dependence on several contributions due to doping (defects), anharmonicities, and ep-interactions. The presence of ep-coupling constant in each term of EHC is an additional and unusual feature of the present formulation. The variation of EHC for La2􀀀xSrxCuO4 and YBa2Cu3O7􀀀 with temperature is reported. The e ects of doping and ep-coupling constant on EHC for both HTS have been investigated carefully and discussed in chapter 5. Chapter 5 is dedicated to the theoretical estimation of the phononic heat capacity (PHC) using the RPDOS via average lattice energy undertaking the e ects of defects, anharmonicities, and ep-interactions. A unique feature of the present theory is that PHC separates into diagonal and non-diagonal components. The obtained results of total heat capacity for La2􀀀xSrxCuO4 and YBa2Cu3O7􀀀 HTS shows a successful agreement between theory and experiment. The doping concentration v and ep-coupling constant dependence on PHC and EHC have been investigated for both HTS. Chapter 6 is devoted to a concise summary of the thesis work onward including the scope of this work. This chapter highlights the most valuable outcomes and presents feasible ways of stimulating future perspectives.